Plato/Gulliver The beginning of Book VII starts off with the allegory of the cave. As Socrates describes this world of the cave to Glaucon, you can see a connection between the allegory and Flatland. The shackled prisoners in the cave know of nothing but the shadows they see before them. To them, this is their "reality." They have no concept of the objects that cast the shadows or the fact that the shadows they see before them are actually cast by anything at all. This is analogous to the inhabitants of Flatland who have no conception of 3-dimensional objects. Such as a 3-dimensional object casts a "shadow" in 2-dimensional space, an inhabitant of Flatland would believe this to be reality and could not comprehend that this "shadow" could be anything other than reality. In this way, the allegory of the cave and the interplay of different dimensions are closely related. Another important side note to this section of Book VII is Plato's comparison of the things the prisoner experiences to the different realms of knowledge. While he does not say what the shadows represent, it can be inferred through the reading that these are mathematical objects (i.e.- triangles, squares, etc... such as can be found for the representation of the male inhabitants of Flatland). If I'm not mistaken, Plato also believed that these were objects of knowledge and not merely belief. Next, Plato compares the trees and mountains the prisoner sees when he is outside the cave to the Forms, these being images that we relate to as we look upon our "reality." Finally, Plato compares the light of the sun to Goodness, though he never specifies what goodness is. In this way, Plato asserts that these different types of knowledge are all interconnected and that the ultimate achievment is that of Goodness. I'm not sure if there is any relation here to Flatland, but the use of mathematical objects (just a guess on my part) and the Forms definitely relates to Abbott's use of objects in Flatland. In the next section, Socrates outlines what type of education needs to take place for rulers. He suggests that they learn mathematics. After all, a truly great ruler must be able to think abstractly. By learning about the Forms a leader can truly make the most of his intellect. He actually lists five types of math: arithmetic, plane geometry, solid geometry, astronomy, and harmonics. Keeping in mind that Pythagoras had done a large amount of work in mathematics at this time, it is obvious the correlations here with Flatland. The basis for much of the mathematics used in Flatland was developed during this time. And the final section of Book VII discusses the need for future leaders to also learn the art of logical argument, also known as dialectic. Much of the logical way that the inhabitants of Flatland are presented is not only a satire on the times, but a relation to this type of logical argumentation.